Modeling and understanding localized nonlinear waves in photonic bandgap structures

Photonic band gap (PBG) structures have originally been explored in electro-optics. During the last five years, 2D planar PBG circuits have also been used at microwave frequencies. PBG structures behave as high impedance surfaces and suppress surface waves in one or more frequency ranges. Until now, these circuits have only been reliably modeled by numerical methods. A new equivalent circuit model is proposed. The model is based on the transmission line theory and periodic structures. The model is simple, but limited as it only allows for determination of the stop bands for the two principal directions of wave propagation. Nevertheless, it is a useful first step in the design of PBG structures. If this model is coupled with a simple numerical modeling using the FDTD method, it predicts the complete characteristics of the structure. The proposed analytical and numerical modeling is applied to improve the performance of a broadband circularly polarized patch antenna.

Summary form only given. Photonic band gap (PBG) materials are artificial, periodic, dielectrics that enable engineering of the most fundamental properties of electromagnetic waves. These include the laws of refraction, diffraction, and spontaneous emission of light. Unlike traditional semiconductors that rely on the propagation of electrons through an atomic lattice. PBG materials execute their novel functions through selective trapping or "localization of light". Three dimensional (3D) PBG materials offer a unique opportunity to simultaneously (i) synthesize micron-scale 3D optical circuits that do not suffer from diffractive losses and (ii) engineer the electromagnetic vacuum density of states in this 3D optical micro-chip. The 3D PBG enables broadband on-chip optical communication in fully three-dimensional optical micro-circuits. Unlike traditional wave-guides that confine light in a high refractive index core by total internal reflection, the circuit paths in a PBG material may consist of air. They guide light through wave interference effects, the hallmark of the localization phenomenon. In the case of the PBG optical circuit, there are three geometrical dimensions for device integration and an additional dimension of frequency bandwidth, whereby hundreds of optical wavelength channels of information can be conveyed in parallel through a single PBG wave-guide. I review recent approaches to micro-fabrication of photonic crystals with a large 3D PBG centered near 1.5 microns. These include direct laser-writing techniques, holographic lithography, silicon double inversion, and a newly invented optical phase mask lithography technique.

Photonic bandgap (PBG) structures constructed from lossy, dispersive dielectric and metallic materials are characterized in terms of their reflection and transmission properties. Particular emphasis is given to PBG structures with defects. These PBG structures are modeled analytically with an ABCD matrix method for their single-frequency response. They also are modeled numerically with a finite-difference time-domain approach to determine their operating characteristics over a wide set of frequencies in a single simulation. It is shown that material dispersion can significantly alter the characteristics of a PBG structure’s frequency response. Metallic PBG structures at optical frequencies thus exhibit bandgap characteristics significantly different from those of their nondispersive dielectric counterparts. It is shown that microcavities whose mirrors are constructed from dispersive-material PBG structures can be designed to outperform similar nondispersive-mirror microcavities.

Photonic band-gap (PBG) materials have recently attracted significant interest in the microwave region to suppress surface waves and to improve component performance. In this article, the NY-FDTD (nonYee grid higher order finite difference time-domain) formulation of a PBG structure in an anisotropic medium is derived, and then applied to compute the dispersion curves of 2D PBG structures. The numerical results for the isotropic medium are in good agreement with that from the traditional FDTD method. Then, the dispersion curves for anisotropic media are provided respectively. Which show that both the TM wave in the PBG structure with a magnetic-anisotropic medium and the TE wave in a PBG structure with an electric-anisotropic medium, possess an enhanced bandwidth of the first band-gap and also an increment of the number of bandgaps, compared to that of a PBG with isotropic medium.

Laser-assisted chemical vapor deposition (LCVD), in combination with 3-D self-assembly of colloidal silica particles, was used to fabricate 3-D photonic bandgap (PBG) structures. Multilayer of colloidal silica particles was formed on silicon substrates using the isothermal heating evaporation approach. A continuous wave (CW) CO2 laser (10.6 µm wavelength) was used as the energy source in the LCVD process. A silica-core-silicon-shell PBG structure was obtained. This technique is capable of fabricating structures with various PBGs by obtaining different silicon shell thickness with different LCVD parameters. This enables us to engineer the position and width of PBGs by flexibly controlling the core-shell geometry. Face-centered cubic (FCC) PBG structures were composed by “effective atom” of silica-core-silicon-shell. In this study, a series of PBG structures with designed PBGs were obtained with different experimental conditions. Incidence-angle-resolved spectroscopic ellipsometer was used to identify specific PBGs. The refractive indices of the “effective atom” with different silicon-shell thickness were calculated using Bruggeman composite model. The plain-wave expansion was used to simulate the photonic dispersion diagrams, which agreed with the experimental results.

Two dimensional metallic photonic band gap (PBG) structures, which have higher power handling capability, have been analyzed for their dispersion characteristics. The analysis has been performed using flnite difierence time domain (FDTD) method based on the regular orthogonal Yee's cell. A simplifled unit cell of triangular lattice PBG structure has been considered for the TE and TM modes of propagation. The EM fleld equations in the standard central-difierence form have been taken in FDTD method. Bloch's periodic boundary conditions have been used by translating the boundary conditions along the direction of periodicity. For the source excitation, a wideband Gaussian pulse has been used to excite the possible modes in the computational domain. Fourier transform of the probed temporal flelds has been calculated which provides the frequency spectrum for a set of wave vectors. The determination of eigenfrequencies from the peaks location in the frequency spectrum has been described. This yields the dispersion diagram which describes the stop and pass bands characteristics. Efiort has been made to describe the estimation of defect bands introduced in the PBG structures. Further, the present orthogonal FDTD results obtained have been compared with those obtained by a more involved non-orthogonal FDTD method. The universal global band gap diagrams for the considered metal PBG structure have been obtained by varying the ratio of rod radius to lattice constant for both polarizations and are found identical with those obtained by other reported methods. Convergence of the analysis has been studied to establish the reliability of the method. Usefulness of these plots in designing the devices using 2-D metal PBG structure has also been illustrated.

We present a photonic band gap (PBG) structure design for terahertz (THz) wave parametric generation, which has crystal layer fabrication tolerance of a few micrometers and can be made with traditional polishing methods. This PBG structure consists of two component materials with a small refractive index difference at near infrared pump wavelengths and a large refractive index difference for THz waves. With this design the PBG device has optical properties very close to that of a bulk crystal in the near infrared, but photonic crystal features in the THz range, such as structural dispersion, which allows placement of the phase matched pump wavelength in the near infrared to eliminate two-photon absorption of the pump and signal beams. The added design flexibility also allows the use of the most efficient crystal orientations. Potential applications of this THz PBG structure are discussed.

We present the theoretical analysis and computer simulation of the wakefields in a 17 GHz photonic band-gap (PBG) structure for accelerator applications. Using the commercial code CST Particle Studio, the fundamental accelerating mode and dipole modes are excited by passing an 18 MeV electron beam through a seven-cell traveling-wave PBG structure. The characteristics of the longitudinal and transverse wakefields, wake potential spectrum, dipole mode distribution, and their quality factors are calculated and analyzed theoretically. Unlike in conventional disk-loaded waveguide (DLW) structures, three dipole modes (${\mathrm{TM}}_{11}$-like, ${\mathrm{TM}}_{12}$-like, and ${\mathrm{TM}}_{13}$-like) are excited in the PBG structure with comparable initial amplitudes. These modes are separated by less than 4 GHz in frequency and are damped quickly due to low radiative $Q$ factors. Simulations verify that a PBG structure provides wakefield damping relative to a DLW structure. Simulations were done with both single-bunch excitation to determine the frequency spectrum of the wakefields and multibunch excitation to compare to wakefield measurements taken at MIT using a 17 GHz bunch train. These simulation results will guide the design of next-generation high-gradient accelerator PBG structures.

A novel one-dimensional (1-D) photonic bandgap (PBG) structure for microstrip lines is proposed. This new circuit is consisting of cross-gaps and base-to-base triangles etched in the ground plane of microstrip line. The PBG structures were designed and fabricated with different dimensions. It has been shown that the stopband characteristics may be controlled by tuning the geometrical dimensions. Also, multiple-frequency-tuned PBG structure has been derived by increasing the geometrical dimension.

In a certain spectral range the extinction coefficient K in n-i-p-i layers becomes negative at the high excitation levels. It results in the appearance of the light amplification. The extinction coefficient in n-i-p-i layers depends on the wavelength and the difference in the quasi-Fermi levels /spl Delta/F. We considered the model, when a pump, which can be electrical as well as optical, excites uniformly all active layers and calculated light transmission characteristics versus /spl Delta/F which is the same within all active layers. In the present work we consider the optical mechanism of the pump, and solve the nonlinear problem of the pump light propagation through the photonic band gap (PBG) structure and the linear problem of a probe light transmission through the same structure with excited active layers.

We introduce a new accelerator cavity design based on Photonic Band Gap (PBG) structures. The PBG cavity consists of a two‐dimensional periodic array of high dielectric, low loss cylinders with a single removal defect, bounded on top and bottom by conducting sheets. We present the results of both numerical simulations and experimental measurements on the PBG cavity.

The self-arrangement of colloidal crystal in the fcc and bcc lattices is one way available to fabricate three dimensional periodic microstructures in the micron- and submicron-size regimes. The photonic band gaps (PBG) structure with its atom composed of two conjugate dielectric sphere in the uniform dielectric medium is revealed to possess full band gap both in fcc and bcc lattices. The photonic band structure is strongly dependent on the direction of the atom axis and there exist for both lattices some favorable directions of atom in opening a full band gap. It is (1,1,1) for fcc lattice and (2,1,0) for bcc lattice. The combination of such a PBG structure with the self-arrangement technique of colloidal crystal can provide a potential to fabricate the three dimensional photonic crystal with a full band gap in the optical regime.

A one-dimensional, single-material polarizing photonic bandgap structure is designed and fabricated using e-beam PVD and oblique angle deposition technique. In order to obtain high- and low-index layers, we deposited alternate layers of titanium dioxide (TiO₂) at deposition angles of 0&deg; and 70&deg;on top of a fused silica substrate. This approach is chosen since at deposition angle of zero degree, deposited TiO₂ using e-beam PVD, show a negligible birefringence while the obliquely deposited TiO₂acts as a biaxial material with significant birefringent behavior. As a result, deposition of a bilayer film at two angles is analogous to using two different materials with the advantage of simplifying fabrication and modeling this polarizing device. The bandgap of the bilayer structure is modeled in a way that only a specific wavelength with certain polarization, <i>p </i>polarization, could pass through while the <i>s </i>polarization is reflected. For modeling we used Transfer Matrix Method and numerical FDTD analysis to simulate behavior of the 1D photonic band gap structure. The simulations produce better than 98% reflection for <i>s</i> polarization and almost no reflection for <i>p</i> polarization for the center wavelength of 632.8 nm. The fabricated device shows 94% reflection for s polarization and less than 6% reflection for <i>p</i> polarization at the red HeNe laser wavelength at an incident angle of 70&deg;. The results demonstrate that a 1D multi-layer photonic crystal, fabricated from a single material, can be designed to selectively reflect or transmit<i> p</i> or<i> s</i> polarization of an incident light beam.

One-dimensional (1-D) photonic bandgap (PBG) structures remain one of the most practical ways of applying the PBG concepts to the solution of many urgent problems in laser physics and optical technologies. The sol-gel method is an inexpensive and flexible liquid phase processing technique that is suitable for the deposition of multilayer stacks. The multilayer stacks can be designed as 1-D PBG structures, such as distributed Bragg reflectors (DBR), or single and coupled microcavities, as reported in this work. Spin-coated TiO2 and SiO2 layers acted as the high and low refractive index materials, respectively. Each layer was heat-treated at a high temperature (~1000 degree(s)C) for a short period of time (~90 s) in order to increase the index contrast, while preserving relatively smooth interfaces between the consecutive layers. Ellipsometry, X-ray diffraction, micro-Raman spectroscopy, transmittance/reflectance spectroscopy, and atomic force microscopy were used to characterize both the individual layers and the whole structures. Strong PBG properties are demonstrated, with an omni-directional stop band for a 5.5-pair DBR ((lambda) equals 550 - 600 nm, gap to mid-gap ratio equals 7.6%) and sharp pass bands within the stop bands for the microcavities.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

We discuss the development of label-free, real-time and low-cost biosensors based on planar photonic bandgap (PBG) structures. We propose a novel power-based readout technique where the PBG shift is indirectly tracked by simply exciting the photonic sensing structure with a filtered broadband source and measuring the output power with a power meter. Therefore, the use of either tunable lasers or spectrum analyzers to continuously acquire the transmission spectrum of the structure, as done for other spectrum-based sensing techniques, is avoided. We have used this technique both for the sensing of refractive index variations as well as for the label-free detection of antibodies, showing high sensitivities and low detection limits, which demonstrate its high potential for the development of label-free, real-time and low-cost photonic biosensors. Furthermore, the use of broadband sources and detectors for the readout of the photonic sensors will also allow their integration, thus achieving a completely electrically accessed photonic biosensing device.